solution_hw2

solution_hw2 - Please notice that the solution below is...

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Please notice that the solution below is just a possible one. Any different solutions which make sense are also welcomed. In the stochastic case, the new model is as below: Maximize 3 123 456 789 1 [1000( ) 750( ) 250( )] j jj jjj j j P yyy = ++ + + Suppose Scenario 1 refers to the normal water allocation, Scenario 2 the 10% higher case and Scenario 3 the 40% lower case. Therefore, 0.5, 0.4, 0.1 PPP = == . And the constraints for ,1 , 2 , 3 ; 1 , 2 9 j i yj i K are And for each i, 0 j ii yx ≤≤ . The constraints for i x are the same as the constraint 1, 3, 4, 5 in the textbook. Solving this linear programming, we can derive the optimal planting decisions shown in table below Allocation (Acres) Kibbutz Crop 1 2 3 Sugar beets 100 180 130 Cotton 180 240 80 Sorghum 0 0 0 And the optimal watering decision under Scenario 1 is (80, 106.7, 71.7, 180, 240, 80, 0, 0, 0); under Scenario 2 is (100, 133.3, 84.2, 180, 240, 80, 0, 0, 0); under Scenario 3 is (0, 0, 21.7, 180, 240, 80, 0, 0, 0). The expected return is \$63333.3. Please notice here there is NOT only one optimal solution to this programming.

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solution_hw2 - Please notice that the solution below is...

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